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Design and Control of Compliant Humanoids
Alin Albu-Schäffer
DLR – German Aerospace CenterInstitute of Robotics and Mechatronics
Torque Controlled Light-weight Robots
Torque sensing in each jointMature technology for experimental platforms
First Applications of the Technology in Automotive Industry
KUKA Demonstrator
Sensor based assembly with the LWR
• Robot commercialized by KUKA since 2008• Fast, open research software interface (FRI) Available since 2010
Gearbox Assembly at Daimler
• Production started 2009 24/7 Application with the LWR• More than 50000 gearbox units in Mercedes cars• Production without fences. Humans interact with the robot
Special Gripper from earlier solutions
Modularity and light-weight allows the constructionof complex kinematics using the arm joints
DLR crawler DLR walker[Ott & al. Humanoids 2010, 2011]
Mechatronic Joint Design
(redundant)
The complete Finger System
The DLR-HIT-handson the way to commercialization
Hand I with four fingers,12 actuators
• tooth belt drives• 1kg finger tip force• torque control
Hand II with five fingers ,15 actuators
DEXHAND –Europe‘s first Robonaut hand
Tendon driven, 12 active dofLess than 3.3 kgFinger length 93 mm (Thumb 100 mm), DEXHAND length 340 mm25 N Fingertip force (Thumb 40 N) –
streched out
25 N test
New light-weight robot withf/t sensing in the joints and at extremities
- Higher power and speed
SARAH
motor dynamics Robotdynamics
f
a
d
BKT
torquecontrol
Impedancecontrol
xd
.
B
Passivity Robustness in contact with the environment
Unified approach for torque, position and impedance control on Cartesian and joint level
Cartesian Impedance Control
FTF K 1)1( BKBB T1)1(
[Albu-Schäffer & al, IJRR 2007]
DLR Hand II – Impedance Control
Joint impedance ControlCartesian Impedance ControlObject Impedance Control
[Wimböck al. IJRR 2010]
Impedance Control for Two Handed Manipulation
Gravitycompensation
)()()( DVgd
Stiffness term Damping term1ms control cycle for the whole system
Human-Robot-Interaction
M
D
Impe
danc
e C
ontro
lA
dmitt
ance
Con
trol
w
vf
Compliant Control of the entire Robot
53 active dof150 kg
Rollin’ Justin
Current Research Plattform based on Variable Compliance Actuation (VIA)
The antagonisticconcept
Load
q1
Motor 2
Motor 1
q2
q
Output
Non linearspring
Link Motion
Stiffness adjustment
Size, force and dynamics of a human arm/handVariable stiffness 52 motors,111 position sensors
Anthropomorphic Hand-Arm-System
No torque sensing: torque observed from positions
A Hand-Arm System for Space Robot Assistrance
Extension of the passivity based control approaches to the VIA robots:Variable, nonlinear stiffnessStrongly coupled joints
The new integrated hand-arm-system(with variable impedance actuation VIA)
Grebenstein & al. Humanoids 2010]
Motor 1
Motor 2
Moving Joint Output
Changing Stiffness
External Load
2 equally sized motorsmotors pull tendons
q
θ1
θ2
Control
IM2
IM1
τLTorque
Estimator
Antagonistic Actuator (fingers)VIA – Variable Impedance Actuators 1
Motor 1
Motor 2
q
Moving Joint OutputChanging Stiffness External Load
NonlinearSprings
2 equally sized motorsboth motors push and pull (bidirectional)
Bidirectional Antagonistic Actuator(underarm rotation and wrist)
VIA – Variable Impedance Actuators 2
[Petit & al. ICRA 2010]
Motor 1
Motor 2
q
Moving Joint Output
Changing Stiffness
External Load
Adjustable Stiffness Actuator (upper arm)
NonlinearSprings
Harmonic Drive Gearone big motor1 moves the jointone small motor2 changes joint stiffnesswithout motor2we have a serial elastic joint
VIA – Variable Impedance Actuators 3
[Wolf & al. ICRA 2008]
Joint Data Sheet: DLR VS-Joint
217°/sMax. Equilibrium Velocity
Variable StiffnessActuator Type
270 + 50 = 320 WNominal Power(not max./peak!)
16.8 JMax. Storable Energy
± 14° / ± 14°Max. Deflection Range (min./max Stiff.)
Ø97x106 / ~ Ø97x166 mmSize (w/wo Motors)
1.4 / ~ 2.0 kgWeight (w/wo Motors)
7.3%Torque Hysteresis at Max. Torque
0.2 sMin. Stiffness Adjusting Time(from 3% to 97% stiffness)
0 / 315 Nm/radMin./Max. Stiffness (no external load)
± 180 NmMaximum Joint Torque(repeatable, evaluated by measurement)
c : Radius of Cam DiskJoint Deflection cφφ
VIACTORS
Joint Data Sheet: DLR QA-Joint
217°/sMax. Equilibrium Velocity
Quasi AntagonisticActuator Type
270 + 50 = 320 WNominal Power(not max./peak!)
2.7 JMax. Storable Energy
± 15° / ± 3°Max. Deflection Range (min./max Stiff.)
Ø90x100 / ~ Ø90x160 mmSize (w/wo Motors)
1.4 / ~ 2.0 kgWeight (w/wo Motors)
+/-12.5%Torque Hysteresis at Max. Torque
0.15 sMin. Stiffness Adjusting Time(from 3% to 97% stiffness)
20 / 550 Nm/radMin./Max. Stiffness (no external load)
± 40 NmMaximum Joint Torque(repeatable, evaluated by measurement)
VIACTORS
Torque [Nm]
Stiffness [Nm/rad]
Validation of Arm Robustness
Control of VIA Joints
useful for cyclic movementsinvolving energy storage
(running or throwing)
damping of the arm for fast,fine positioning tasks has to be
realized by control.
The joints have very low intrinsic damping
Ensuring the achievement of the desired link position with motorposition based control.Providing the desired stiffness property.
General Model
For all considered actuator types so far, following model structure holds
Main properties:- under-actuation: less control inputs ( ) than dimension of
configuration space- positive definiteness of
2,1
We propose this generic model for controller design of VIA joints
External disturbance torque
)(xV
Flexible joint model is a particular case[Albu-Schäffer at ICRA 2010]
Decoupling in Modal Coordinates
11~ KKKKKKu STDP
TSQS
TTQT
TDQD
TPQP
QKQK
QKQK
QKQK
QQKK
back to link coordinatessymmetric,nondiagonalp.d
state feedback controller in link coordinates.
[Petit at ICRA 2010]
Experimental Validation
Vibration Damping OFF Vibration ON
Point to Point trajectory
Experimental Validation
Cartesian Impedance Control
Potential:
Damping design:Double diagonalization of the inertia matrix and the Hessian of the potential function.
qqDqqVqgτm )()()(
Implementation of a simple Cartesian impedance
),),(()( ddS HqHVqV dK
dH
)(qH
6extF
Extension for variable stiffness joints
Combine active and passive impedance
[Petit at IROS11]
Passive Joint Elasticities & Cartesian Stiffness
diagonal
bounded
generate by passive joint stiffness
severe limitation of achievable Cartesian stiffnesserror: 25-55%
[Albu-Schäffer et al. 03]
Cartesian transformation
Combining Active & Passive Impedances
active impedancecontroller
best of both worlds:overcome limitations of passive stiffnessget VSA features
passive jointstiffness
1. Step: Passive Compliance Optimization
achieve Cartesian compliance as good as possible by passive compliance
least-squares problem
solution by active-set algorithmefficient (pseudo inverse)fast (366Hz for 4 joints)
residualpassive
compliance
2. Step: Active Compliance Optimization
remove residual by active compliance
optimization formulation:
solution by matrix nearness problemefficient (eigenvalue problem)
possibly negative definite stability issues
.. goal matrix
.. positive definite
[Higham 98]
Results
passive spring dominant:motion provided by link
active spring dominant:motion provided by motor
motor pos
link pos
Performance ValidationVIA jointRigid joint
Optimal control for maximizing endvelocity.- Analytical solutions for 1dof, linear case- Extension to nonlinear case with dynamicconstraints
Constant vs. Variable Stiffness
Increase in velocity for the QA joint
[Haddadin at IFAC 2011]
Performance Validation for multi dof2 dof system
ball throwing
Evaluation of human-inspiredthrowing motion generation
Performance Demonstration with the Hand
Chalon & al. IROS 2011
Performance Validation: Kicking Experiments
Experimental Results
Impact joint torque
Kicking range
Speed
10 Nm85 Nm
4.05 m1.6 m
6.35 m/s3.06 m/s
VS-JointStiff Joint
WP2- Robotics of Biological Neuro-mechanical Control
Imperial College London[Ganesh & al., TRO 2011]
The DLR Hand-Arm System